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The aim of this thesis is the stiffness analysis of cable-driven parallel robots. Cable-driven parallel robots have drawn considerable attention because of their unique abilities and advantages such as the large workspace, light weight of cable actuators, easy disassembly and transportation of the robot. The mobile platform of a cable-driven parallel robot is attached to the base with multiple cables. One of the parameters that should be studied to make sure a robot is able to execute a task accurately is stiffness of the robot. In order to investigate the stiffness behaviour of a robot, the stiffness matrix can be calculated as the first step. Because cables act in tension, keeping the positive tension in cables becomes a challenge. In order to have a fully controllable robot, an actuation redundancy is needed. These complexities are addressed in the thesis and simulations. In this thesis, the complete form of the stiffness matrix is considered without neglecting any terms in calculation of the stiffness. Some stiffness indices such as single-dimensional stiffness based on stiffness ellipse, directional stiffness and condition number of the stiffness matrix are introduced and calculated and stiffness maps of the robot are developed. In addition, the issue of unit inconsistency in calculating the stiffness index is addressed. One of the areas which is also addressed in this thesis is failure analysis based on the stiffness of robot. The effect of the failure in one or more cables or motors is modelled and stiffness maps are developed for the failure situation. It is shown that by changing the anchor position and mobile platform orientation, the lost stiffness after failure of a cable or motor can be retrieved partially. Optimum anchor position and mobile platform orientation are identified to maximize the area of the stiffness map. Condition number of the stiffness matrix while robot is following a trajectory is optimized. In addition, when one cable fails during the path planning, the recovery of the robot is studied. Finally, these analyses on stiffness and failure provide the designer with the necessary and valuable information about the anchor positions and actuator toques. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2013-04-27 08:47:26.297

Cable robots are a type of robotic manipulator that has recently attracted interest for large workspace manipulation tasks. Cable robots are relatively simple in form, with multiple cables attached to a mobile platform or end-effector. The end-effector is manipulated by motors that can extend or retract the cables. Cable robots have many desirable characteristics, including low inertial properties, high payload-to-weight ratios, potentially vast workspaces, transportability, ease of disassembly/reassembly, reconfigurability and economical construction and maintenance. However, relatively few analytical tools are available for analyzing and designing these manipulators. This thesis focuses on expanding the existing theoretical framework for the design and analysis of cable robots in two areas: disturbance robustness and workspace generation. Underconstrained cable robots cannot resist arbitrary external disturbances acting on the end-effector. Thus a disturbance robustness measure for general underconstrained single-body and multi-body cable robots is presented. This measure captures the robustness of the manipulator to both static and impulsive disturbances. Additionally, a wrench-based method of analyzing cable robots has been developed and is used to formulate a method of generating the Wrench-Feasible Workspace of cable robots. This workspace consists of the set of all poses of the manipulator where a specified set of wrenches (force/moment combinations) can be exerted. For many applications the Wrench-Feasible Workspace constitutes the set of all usable poses. The concepts of robustness and workspace generation are then combined to introduce a new workspace: the Specified Robustness Workspace. This workspace consists of the set of all poses of the manipulator that meet or exceed a specified robustness value.

Les Robots Parallèles à Câbles (RPC) sont particulièrement adaptés pour des applications telles que le transport de charges lourdes au travers de grands espaces de travail. Afin de contrôler l'ensemble des degrés de liberté de la plate-forme tout en optimisant la taille de l'espace de travail du robot par rapport au volume de sa structure, la redondance d'actionnement est nécessaire. Dans cette thèse, un algorithme de distribution des tensions des câbles compatible temps-réel est introduit. Il permet de calculer efficacement différentes solutions optimales au problème de la distribution des tensions des RPC à deux degrés de redondance. Des schémas de commande adaptés aux RPC, intégrant l'algorithme de distribution des tensions, sont ensuite proposés. Un schéma de commande en espace double est introduit pour compenser la dynamique de la plate-forme et des enrouleurs. Afin de pallier les incertitudes et les variations des paramètres des modèles, une commande adaptative en espace double est finalement proposée. Des résultats expérimentaux prouvent la compatibilité temps-réel des algorithmes et des lois de commande développés dans cette thèse, ainsi que leur stabilité le long de la trajectoire suivie. / Cable-driven parallel robots (CDPR) are particularly well adapted for some applications such as handling of heavy payloads over large workspaces. However, in order to fully control all the degrees of freedomof the mobile platformand to obtain large workspace to footprint ratios, redundant actuation may be required, which implies the determination of feasible cable tension distributions. In this thesis, in the case of CDPR with two degrees of actuation redundancy, real-time compatible algorithms capable of efficiently calculating various continuous tension distribution are introduced. Furthermore, efficient control schemes are proposed in order to increase the CDPR tracking performances. First, an dual-space feedforward control scheme is introduced to compensate for the plate-formeand whinches dynamics. In order to deal with parametric variations and incertainties in the models, an adaptive dual-space motion control scheme for CDPR is finally presented. Experimental results validate the reel-time efficiency of the proposed tension distribution algorithmand control schemes as well as their stability along the tracked trajectory.

Dans cette thèse, un stabilisateur actif est conçu pour être embarqué sur la plate-forme d'un Robot Parallèle à Câbles (RPC) et compenser les vibrations de la plate-forme en produisant un torseur d’effort sur celle-ci. Tout d’abord, une modélisation mécanique de divers dispositifs de stabilisation actifs permet de choisir une solution appropriée à la compensation des vibrations. La solution sélectionnée consiste en un stabilisateur composé de bras en rotation. Ensuite, ce modèle est utilisé pour optimiser la structure du stabilisateur en recherchant quelle disposition de ses bras permet de maximiser la puissance fournie par le stabilisateur à la plate-forme mobile du RPC.Une stratégie de commande est alors proposée pour contrôler le système composé de la plate-forme mobile du RPC et du stabilisateur actif embarqué. Ce système étant constitué de deux parties fonctionnant à des échelles de temps différentes, la théorie de la perturbation singulière est utilisée pour prouver la stabilité de la commande proposée.Enfin, des expériences en simulation permettent de valider l’utilisation d’un stabilisateur actif embarqué pour la compensation des vibrations de la plate-forme mobile d’un RPC et commandé avec la loi de commande proposée dans cette thèse. / In this thesis, an active stabilizer is designed to be embedded on the platform of a Cable-Driven Parallel Robot (CDPR) and to damp vibrations affecting the platform by producing a wrench on it.First, a mechanical modeling of various active stabilization devices allows the choice of an appropriate solution for vibration damping. The selected solution consists of a stabilizer composed of rotating arms. Then, this model is used to optimize the stabilizer structure by looking at which arm arrangement maximizes the power delivered by the stabilizer to the CDPR mobile platform.A control strategy is then proposed for the system consisting of the CDPR mobile platform and the embedded active stabilizer. As this system consists of two parts operating at different time scales, the singular perturbation theory is used to prove the stability of the proposed control.Finally, simulation experiments make it possible to validate the use of an on-board active stabilizer to damp the vibrations of the mobile platform of a CDPR, and controlled with the control law proposed in this thesis.

In this thesis, the redundancy resolution and failure analysis of Cable-Driven Parallel Manipulators (CDPM) are investigated. A CDPM consists mainly of a Mobile Platform (MP) actuated by cables. Cables can only apply force in the form of tension. So, to design a fully controllable CDPM, the manipulator has to be redundantly actuated (e.g., by using redundant cables, external force/moment or gravity). In this research, the redundancy resolution of planar CDPMs is investigated at the kinematic and dynamic levels in order to improve the manipulator safety, reliability and performance, e.g., by avoiding large tension in the cables that may result in high impact forces, and avoiding large MP velocities that may cause instability in the manipulator, or on the contrary, by increasing the cable tensions and the stiffness for high-precision applications. The proposed approaches are utilized in trajectory planning, design of controllers, and safe dynamic workspace analysis where collision is imminent and the safety of humans, objects and the manipulator itself are at risk. The kinematic and dynamic models of the manipulator required in the design and control of manipulators are examined and simulated under various operating conditions and manufacturing automation tasks to predict the behaviour of the CDPM. In the presented research, some of the challenges associated with the redundancy resolution are resolved including positive tension requirement in each cable, infinite inverse dynamic solutions, slow-computation abilities when using optimization techniques, failure of the manipulator, and elasticity of cables that has a significant role in the dynamics of a heavy loaded manipulator with a large workspace. Optimization-based and non-optimization-based techniques are employed to resolve the redundancy of CDPM. Depending on the advantages and disadvantages of each method, task requirements, the used redundancy resolution technique, and the objective function suitable optimization-based and non-optimization-based routines are employed. Methodologies that could combine redundancy resolution techniques at various levels (e.g., position, velocity, acceleration, and torque levels) are proposed. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2012-09-26 22:39:34.35

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Les Robots Parallèles à Câbles sont des robots possédant un effecteur relié à une base uniquement à l’aide de câbles, dont il est possible de modifier la longueur. Ils sont ainsi légers, capables de grandes dynamiques et peuvent présenter un énorme espace de travail.Mais ils sont sujets à des vibrations de grande amplitude et basse fréquence à cause de leur rigidité très faible. Cette thèse propose une approche originale d'amortissement actif pour atténuer efficacement ces vibrations. Le modèle dynamique du robot à câbles embarquant des roues à inertie est calculé, linéarisé autour d'un point d'équilibre et projeté dans l'espace modal dans lequel les vibrations sont découplées. Une commande par placement de pôles adapté à la fréquence naturelle de vibrations est appliquée pour chaque mode. Les résultats sur une simulation et deux prototypes sont présentés pour valider cette approche. / Cable-driven parallel robots use cables only to connect a fixed base to a mobile end-effector. Robot motion is obtained by winding the cables around pulleys to alter their length. Thus, cable-driven parallel robots are lightweight, can achieve very high dynamics and exhibit a very large workspace.Therefore, they are subject tp high magnitude and low frequency vibrations, because of their very low end-effector stiffness.This thesis proposes a novel approach for effective active damping of those vibrations.The dynamical model of a cable-driven parallel robot embedding reaction wheels is derived, lineraized around an equilibrium point and projected onto modal space, in which vibrations are decoupled.For each vibration mode, a control algorithm designed by poles placement adapted to the associated vibration natural frequency is applied for active vibration damping.Experiments conducted on a realistic simulation and two prototypes are presented to validate this approach.